1 | Basic Concepts on Matrices and Vectors (1) | |
2 | Basic Concepts on Matrices and Vectors (2) | |
3 | Basic Concepts on Matrices and Vectors (3) | |
4 | Basic Concepts on Matrices and Vectors (4) | |
5 | Basic Concepts on Matrices and Vectors (5) | |
6 | System of Linear Equations (1) | |
7 | System of Linear Equations (2) | |
8 | Gaussian Elimination (1) | |
9 | Gaussian Elimination (2) | |
10 | The language of set theory | |
11 | Span of a Set of Vectors (1) | |
12 | Span of a Set of Vectors (2) | |
13 | Linear Dependence and Linear Independence (1) | |
14 | Linear Dependence and Linear Independence (2) | |
15 | Matrix Multiplication | |
16 | Invertibility and Elmentary Matrices | |
17 | Column Correspondence Theorem | |
18 | The Inverse of a Matrix (1) | |
19 | The Inverse of a Matrix (2) | |
20 | Linear Transformations and Matrices (1) | |
21 | Linear Transformations and Matrices (2) | |
22 | Composition and Invertibility of Linear Transformations (1) | |
23 | Composition and Invertibility of Linear Transformations (2) | |
24 | Determinants (1) | |
25 | Determinants (2) | |
26 | Subspaces and their properties | |
27 | Basis and Dimension (1) | |
28 | Basis and Dimension (2) | |
29 | The Dimension of Subspaces associated with a Matrix | |
30 | Coordinate Systems | |
31 | Matrix Representations of Linear Operators | |
32 | Eigenvalues, Eigenvectors, and Diagonalization | |
33 | The Characteristic Polynomial (1) | |
34 | The Characteristic Polynomial (2) | |
35 | Diagonalization of Matrices (1) | |
36 | Diagonalization of Matrices (2) | |
37 | The Geometry of Vectors Dot Product (1) | |
38 | The Geometry of Vectors Dot Product (2) | |
39 | Orthogonal Vectors (1) | |
40 | Orthogonal Vectors (2) | |
41 | Orthogonal Projections (1) | |
42 | Orthogonal Projections (2) | |
43 | Least Squares Approximations and Orthogonal Projection Matrices | |
44 | Orthogonal Matrices and Operators | |
45 | Symmetric Matrices (1) | |
46 | Symmetric Matrices (2) | |
47 | Symmetric Matrices (3) | |
48 | Symmetric Matrices (4) | |
49 | Vector Spaces and Their Subspaces (1) | |
50 | Vector Spaces and Their Subspaces (2) | |
51 | Vector Spaces and Their Subspaces (3) | |
52 | Vector Spaces and Their Subspaces (4) | |
53 | Linear Transformation (1) | |
54 | Linear Transformation (2) | |
55 | Linear Transformation (3) | |
56 | Basis and Dimension (1) | |
57 | Basis and Dimension (2) | |
58 | Basis and Dimension (3) | |
59 | Matrix Representations of Linear Operators (1) | |
60 | Matrix Representations of Linear Operators (2) | |
61 | The Matrix Representations of the Inverse of an Invertible Linear Operator (1) | |
62 | The Matrix Representations of the Inverse of an Invertible Linear Operator (2) | |
63 | Eigenvalues and Eigenvectors of a Matrix Representations of a Linear Operator | |
64 | Inner Product Spaces (1) | |
65 | Inner Product Spaces (2) | |
66 | Inner Product Spaces (3) | |
67 | Inner Product Spaces (4) | |
68 | Inner Product Spaces (5) | |